{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:WZ3FU7LH7WEBPXVVRYYGIJKPC3","short_pith_number":"pith:WZ3FU7LH","schema_version":"1.0","canonical_sha256":"b6765a7d67fd8817deb58e3064254f16cb58a652a872a769a892dab2b2957ab4","source":{"kind":"arxiv","id":"1408.5651","version":3},"attestation_state":"computed","paper":{"title":"Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Yan-kui Bai, Yuan-Fei Xu, Z. D. Wang","submitted_at":"2014-08-25T02:01:08Z","abstract_excerpt":"We show exactly that the squared entanglement of formation (SEF) obeys a set of hierarchical monogamy relations for an arbitrary $N$-qubit mixed state. Based on this set of monogamy relations, we are able to construct the set of hierarchical multipartite entanglement indicators for $N$-qubit states, which still work well even when the concurrence-based indicators lose efficacy. As a by-product, an intriguing analytical relation between the entanglement of formation (EOF) and squared concurrence (SC) for an arbitrary mixed state of $2\\otimes d$ systems is derived, making the concurrence calcula"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.5651","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-25T02:01:08Z","cross_cats_sorted":[],"title_canon_sha256":"cf25c461406f83038b8ed8431824d2e4158b65494a9426979514f74d1b7bfaf5","abstract_canon_sha256":"d33a012b86948295b3124adc02ea4ff43a6fd8df51579c9ae7a706cfc92a7f8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:13.446135Z","signature_b64":"MH8yE3gn5W1wKuECm5Xxl8mfU3zCGEJfebjTQ3XFb5jtk0OMFQg2C4kbgY4hm9cmWUhvrtqo7tWS40p6e5C/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6765a7d67fd8817deb58e3064254f16cb58a652a872a769a892dab2b2957ab4","last_reissued_at":"2026-05-18T01:42:13.445422Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:13.445422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Yan-kui Bai, Yuan-Fei Xu, Z. D. Wang","submitted_at":"2014-08-25T02:01:08Z","abstract_excerpt":"We show exactly that the squared entanglement of formation (SEF) obeys a set of hierarchical monogamy relations for an arbitrary $N$-qubit mixed state. Based on this set of monogamy relations, we are able to construct the set of hierarchical multipartite entanglement indicators for $N$-qubit states, which still work well even when the concurrence-based indicators lose efficacy. As a by-product, an intriguing analytical relation between the entanglement of formation (EOF) and squared concurrence (SC) for an arbitrary mixed state of $2\\otimes d$ systems is derived, making the concurrence calcula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5651","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.5651","created_at":"2026-05-18T01:42:13.445548+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.5651v3","created_at":"2026-05-18T01:42:13.445548+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5651","created_at":"2026-05-18T01:42:13.445548+00:00"},{"alias_kind":"pith_short_12","alias_value":"WZ3FU7LH7WEB","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WZ3FU7LH7WEBPXVV","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WZ3FU7LH","created_at":"2026-05-18T12:28:54.890064+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WZ3FU7LH7WEBPXVVRYYGIJKPC3","json":"https://pith.science/pith/WZ3FU7LH7WEBPXVVRYYGIJKPC3.json","graph_json":"https://pith.science/api/pith-number/WZ3FU7LH7WEBPXVVRYYGIJKPC3/graph.json","events_json":"https://pith.science/api/pith-number/WZ3FU7LH7WEBPXVVRYYGIJKPC3/events.json","paper":"https://pith.science/paper/WZ3FU7LH"},"agent_actions":{"view_html":"https://pith.science/pith/WZ3FU7LH7WEBPXVVRYYGIJKPC3","download_json":"https://pith.science/pith/WZ3FU7LH7WEBPXVVRYYGIJKPC3.json","view_paper":"https://pith.science/paper/WZ3FU7LH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.5651&json=true","fetch_graph":"https://pith.science/api/pith-number/WZ3FU7LH7WEBPXVVRYYGIJKPC3/graph.json","fetch_events":"https://pith.science/api/pith-number/WZ3FU7LH7WEBPXVVRYYGIJKPC3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WZ3FU7LH7WEBPXVVRYYGIJKPC3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WZ3FU7LH7WEBPXVVRYYGIJKPC3/action/storage_attestation","attest_author":"https://pith.science/pith/WZ3FU7LH7WEBPXVVRYYGIJKPC3/action/author_attestation","sign_citation":"https://pith.science/pith/WZ3FU7LH7WEBPXVVRYYGIJKPC3/action/citation_signature","submit_replication":"https://pith.science/pith/WZ3FU7LH7WEBPXVVRYYGIJKPC3/action/replication_record"}},"created_at":"2026-05-18T01:42:13.445548+00:00","updated_at":"2026-05-18T01:42:13.445548+00:00"}